gap> F:=FreeGroup(2);; f1:=F.1;; f2:=F.2;;
gap> G := F / [ f2^100, f1^2, f2*f1*f2^-99*f1^-1 ];;
gap> Size(G);
200
gap> AsList(G);
[ <identity ...>, <[ [ 1, 1 ] ]|f2>, <[ [ 1, -1 ] ]|f2^-1>, 
  <[ [ 1, 2 ] ]|f2^2>, <[ [ 1, -2 ] ]|f2^-2>, <[ [ 1, 3 ] ]|f2^3>, 
  <[ [ 1, -3 ] ]|f2^-3>, <[ [ 1, 4 ] ]|f2^4>, <[ [ 1, -4 ] ]|f2^-4>, 
  <[ [ 1, 5 ] ]|f2^5>, <[ [ 1, -5 ] ]|f2^-5>, <[ [ 1, 6 ] ]|f2^6>, 
  <[ [ 1, -6 ] ]|f2^-6>, <[ [ 1, 7 ] ]|f2^7>, <[ [ 1, -7 ] ]|f2^-7>, 
  <[ [ 1, 8 ] ]|f2^8>, <[ [ 1, -8 ] ]|f2^-8>, <[ [ 1, 9 ] ]|f2^9>, 
  <[ [ 1, -9 ] ]|f2^-9>, <[ [ 1, 10 ] ]|f2^10>, <[ [ 1, -10 ] ]|f2^-10>, 
  <[ [ 1, 11 ] ]|f2^11>, <[ [ 1, -11 ] ]|f2^-11>, <[ [ 1, 12 ] ]|f2^12>, 
  <[ [ 1, -12 ] ]|f2^-12>, <[ [ 1, 13 ] ]|f2^13>, <[ [ 1, -13 ] ]|f2^-13>, 
  <[ [ 1, 14 ] ]|f2^14>, <[ [ 1, -14 ] ]|f2^-14>, <[ [ 1, 15 ] ]|f2^15>, 
  <[ [ 1, -15 ] ]|f2^-15>, <[ [ 1, 16 ] ]|f2^16>, <[ [ 1, -16 ] ]|f2^-16>, 
  <[ [ 1, 17 ] ]|f2^17>, <[ [ 1, -17 ] ]|f2^-17>, <[ [ 1, 18 ] ]|f2^18>, 
  <[ [ 1, -18 ] ]|f2^-18>, <[ [ 1, 19 ] ]|f2^19>, <[ [ 1, -19 ] ]|f2^-19>, 
  <[ [ 1, 20 ] ]|f2^20>, <[ [ 1, -20 ] ]|f2^-20>, <[ [ 1, 21 ] ]|f2^21>, 
  <[ [ 1, -21 ] ]|f2^-21>, <[ [ 1, 22 ] ]|f2^22>, <[ [ 1, -22 ] ]|f2^-22>, 
  <[ [ 1, 23 ] ]|f2^23>, <[ [ 1, -23 ] ]|f2^-23>, <[ [ 1, 24 ] ]|f2^24>, 
  <[ [ 1, -24 ] ]|f2^-24>, <[ [ 1, 25 ] ]|f2^25>, <[ [ 1, -25 ] ]|f2^-25>, 
  <[ [ 1, 26 ] ]|f2^26>, <[ [ 1, -26 ] ]|f2^-26>, <[ [ 1, 27 ] ]|f2^27>, 
  <[ [ 1, -27 ] ]|f2^-27>, <[ [ 1, 28 ] ]|f2^28>, <[ [ 1, -28 ] ]|f2^-28>, 
  <[ [ 1, 29 ] ]|f2^29>, <[ [ 1, -29 ] ]|f2^-29>, <[ [ 1, 30 ] ]|f2^30>, 
  <[ [ 1, -30 ] ]|f2^-30>, <[ [ 1, 31 ] ]|f2^31>, <[ [ 1, -31 ] ]|f2^-31>, 
  <[ [ 1, 32 ] ]|f2^32>, <[ [ 1, -32 ] ]|f2^-32>, <[ [ 1, 33 ] ]|f2^33>, 
  <[ [ 1, -33 ] ]|f2^-33>, <[ [ 1, 34 ] ]|f2^34>, <[ [ 1, -34 ] ]|f2^-34>, 
  <[ [ 1, 35 ] ]|f2^35>, <[ [ 1, -35 ] ]|f2^-35>, <[ [ 1, 36 ] ]|f2^36>, 
  <[ [ 1, -36 ] ]|f2^-36>, <[ [ 1, 37 ] ]|f2^37>, <[ [ 1, -37 ] ]|f2^-37>, 
  <[ [ 1, 38 ] ]|f2^38>, <[ [ 1, -38 ] ]|f2^-38>, <[ [ 1, 39 ] ]|f2^39>, 
  <[ [ 1, -39 ] ]|f2^-39>, <[ [ 1, 40 ] ]|f2^40>, <[ [ 1, -40 ] ]|f2^-40>, 
  <[ [ 1, 41 ] ]|f2^41>, <[ [ 1, -41 ] ]|f2^-41>, <[ [ 1, 42 ] ]|f2^42>, 
  <[ [ 1, -42 ] ]|f2^-42>, <[ [ 1, 43 ] ]|f2^43>, <[ [ 1, -43 ] ]|f2^-43>, 
  <[ [ 1, 44 ] ]|f2^44>, <[ [ 1, -44 ] ]|f2^-44>, <[ [ 1, 45 ] ]|f2^45>, 
  <[ [ 1, -45 ] ]|f2^-45>, <[ [ 1, 46 ] ]|f2^46>, <[ [ 1, -46 ] ]|f2^-46>, 
  <[ [ 1, 47 ] ]|f2^47>, <[ [ 1, -47 ] ]|f2^-47>, <[ [ 1, 48 ] ]|f2^48>, 
  <[ [ 1, -48 ] ]|f2^-48>, <[ [ 1, 49 ] ]|f2^49>, <[ [ 1, -49 ] ]|f2^-49>, 
  <[ [ 1, 50 ] ]|f2^50>, f1, f2*f1, f2^-1*f1, f2^2*f1, f2^-2*f1, f2^3*f1, 
  f2^-3*f1, f2^4*f1, f2^-4*f1, f2^5*f1, f2^-5*f1, f2^6*f1, f2^-6*f1, f2^7*f1, 
  f2^-7*f1, f2^8*f1, f2^-8*f1, f2^9*f1, f2^-9*f1, f2^10*f1, f2^-10*f1, 
  f2^11*f1, f2^-11*f1, f2^12*f1, f2^-12*f1, f2^13*f1, f2^-13*f1, f2^14*f1, 
  f2^-14*f1, f2^15*f1, f2^-15*f1, f2^16*f1, f2^-16*f1, f2^17*f1, f2^-17*f1, 
  f2^18*f1, f2^-18*f1, f2^19*f1, f2^-19*f1, f2^20*f1, f2^-20*f1, f2^21*f1, 
  f2^-21*f1, f2^22*f1, f2^-22*f1, f2^23*f1, f2^-23*f1, f2^24*f1, f2^-24*f1, 
  f2^25*f1, f2^-25*f1, f2^26*f1, f2^-26*f1, f2^27*f1, f2^-27*f1, f2^28*f1, 
  f2^-28*f1, f2^29*f1, f2^-29*f1, f2^30*f1, f2^-30*f1, f2^31*f1, f2^-31*f1, 
  f2^32*f1, f2^-32*f1, f2^33*f1, f2^-33*f1, f2^34*f1, f2^-34*f1, f2^35*f1, 
  f2^-35*f1, f2^36*f1, f2^-36*f1, f2^37*f1, f2^-37*f1, f2^38*f1, f2^-38*f1, 
  f2^39*f1, f2^-39*f1, f2^40*f1, f2^-40*f1, f2^41*f1, f2^-41*f1, f2^42*f1, 
  f2^-42*f1, f2^43*f1, f2^-43*f1, f2^44*f1, f2^-44*f1, f2^45*f1, f2^-45*f1, 
  f2^46*f1, f2^-46*f1, f2^47*f1, f2^-47*f1, f2^48*f1, f2^-48*f1, f2^49*f1, 
  f2^-49*f1, f2^50*f1 ]

# Issue #6031 - too small max. cosets
gap> F := FreeGroup("x", "y", "z");;
gap> R := ParseRelators(GeneratorsOfGroup(F), 
> "x^25=y^25=z^125=1, [x,y]=1, z^y=z^6, z^x=y^5*z, x^5=z^50");;
gap> H_F := F/R;;
gap> H := Image(IsomorphismPcGroup(H_F));
<pc group of size 15625 with 6 generators>
